# Series Coupling Capacitor as Impedance Inverter of Resonator

• Sandbo
In summary, Pozar explains that a series coupling capacitor in a resonator can "invert" the driving point impedance, causing the resonator to act like a series RLC circuit. This can be confusing when simulating the resonator, as the input impedance can peak and then decline.
Sandbo
Hi,

I have been having this question for a long while.
From Pozar's book (Microwave Engineering), on page 336, when he was solving for the resonance response and the Q factor for a Lamba/2 resonator terminated by an open circuit, and coupled to the feed line through a series capacitor, at some points he mentioned:

"...an uncoupled lambda/2 open-circuited transmission line resonator looks like a parallel RLC circuit near resonance, however, in the present case, the series coupling capacitor has the effect of inverting the driving point impedance, thus the response is now like a series RLC resonator..."

I didn't really understand how this happens with a series capacitor.

My understanding was such that, with having a series capacitor, I should take the points where the input impedance being zero (or lowest) as the resonance point, as frequency goes up the series coupling capacitor will any way make the input impedance infinite. (thus it doesn't make sense to consider a parallel RLC circuit which resonates with infinite (or highest) input impedance).

These days I was considering a series capacitively coupled short-circuited transmission line resonator (differs only from the above by the terminator)
What puzzled me further was, when I was simulating the above in HFSS, and plotting the Magnitude of the Input Impedance, I can see it going down slightly then going up a lot to form a peak. That way it in fact looks more like a parallel RLC circuit to me.

How should I perceive the concept of series coupling capacitor as impedance inverter?
And to apply it to various transmission line resonator?

Thanks a lot for your kind attention and my apology for the long post.
Any response would be much appreciated.

Sorry Sandbo, but it has to be a wrong page or a wrong edition. Do you use the forth edition ?

Microwave Engineering by David M.Pozar fourth edition [2012?].

By-the-way, it is a very interesting and complete manual.

However, I am not an expert in microwave engineering. My field it is only power systems.

## 1. What is a Series Coupling Capacitor as an Impedance Inverter of Resonator?

A Series Coupling Capacitor is a type of capacitor that is used to connect two circuits together, allowing the signal from one circuit to flow into the other. It is used as an impedance inverter in resonators to change the impedance of the circuit and achieve resonance at a desired frequency.

## 2. How does a Series Coupling Capacitor work as an Impedance Inverter?

The Series Coupling Capacitor is connected in series with the resonator circuit, creating a voltage divider. This causes the impedance of the circuit to decrease, allowing the resonator to achieve resonance at a lower frequency. This inverter effect is achieved because the capacitor acts as a high-pass filter, allowing high frequencies to pass through while blocking low frequencies.

## 3. What are the benefits of using a Series Coupling Capacitor as an Impedance Inverter?

There are several benefits to using a Series Coupling Capacitor as an Impedance Inverter. It allows for precise tuning of the resonator at a desired frequency, reduces unwanted harmonics in the circuit, and can improve the overall stability of the circuit by providing a more ideal impedance match.

## 4. What types of circuits are commonly used with a Series Coupling Capacitor as an Impedance Inverter?

Series Coupling Capacitors are commonly used in RF (Radio Frequency) circuits, such as in radio receivers and transmitters, as well as in audio circuits, such as in guitar amplifiers and audio filters. They can also be used in oscillators and other electronic circuits that require precise tuning.

## 5. Are there any drawbacks to using a Series Coupling Capacitor as an Impedance Inverter?

While there are many benefits to using a Series Coupling Capacitor as an Impedance Inverter, there are also some potential drawbacks. If not properly designed or chosen, the capacitor can introduce unwanted noise or distortion into the circuit. Additionally, the capacitor may need to be replaced or adjusted if the desired frequency of the resonator changes.

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